﻿ Equivalent Fractions Worksheet | Problems & Solutions Equivalent Fractions Worksheet

Equivalent Fractions Worksheet
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1.
Find the missing number.
$\frac{1}{5}$ = $\frac{n}{15}$ a. 2 b. 4 c. 3 d. 15

Solution:

1 / 5 = n15
[Original algebraic equation.]

1×3 / 5×3 = n15.
[ Multiply both the numerator and the denominator of 1 / 5 by 3 to make the denominators of both the fractions equal.]

3 / 15 = n15

As both the fractions and the denominators are equal, the numerators should be equal.

n = 3

So, the value of the missing number is 3.

2.
Find the missing number. $\frac{3}{8}$ = $\frac{n}{16}$ a. 6 b. 1 c. 3 d. 8

Solution:

3 / 8 = n16
[Original algebraic equation.]

3×2 / 8×2 = n16.
[Multiply both the numerator and the denominator of 3 / 8 by 2 to make the denominators of both the fractions equal.]

6 / 16 = n16

As both the fractions and the denominators are equal, the numerators should be equal.

n = 6

So, the value of the missing number is 6.

3.
Find the missing number. $\frac{7}{8}$ = $\frac{n}{16}$ a. 14 b. 16 c. 8 d. 7

Solution:

7 / 8 = n16
[Original algebraic equation.]

7×2 / 8×2 = n16
[Multiply both the numerator and the denominator of 7 / 8 by 2 to make the denominators of both the fractions equal.]

14 / 16 = n16

As both the fractions and the denominators are equal, the numerators should be equal.

n = 14

So, the value of the missing number is 14.

4.
Find the missing number. $\frac{5}{3}$ = $\frac{n}{9}$ a. 16 b. 15 c. 17 d. 18

Solution:

5 / 3 = n9
[Original algebraic equation.]

5×3 / 3×3 = n9
[Multiply both the numerator and the denominator of 5 / 3 by 3 to make the denominators of both the fractions equal.]

15 / 9 = n9

As both the fractions and the denominators are equal, the numerators should be equal.

n = 15

So, the value of the missing number is 15.

5.
Find the missing number. $\frac{1}{5}$ = $\frac{n}{10}$ a. 8 b. 1 c. 10 d. 2

Solution:

1 / 5 = n10
[Original algebraic equation.]

1×2 / 5×2 = n10
[Multiply both the numerator and the denominator of 1 / 5 by 2 to make the denominators of both the fractions equal.]

2 / 10 = n10

As both the fractions and the denominators are equal, the numerators should be equal.

n = 2

So, the value of the missing number is 2.

6.
Which of the figures represent equivalent fractions?  a. first and third b. all the three c. first and second d. second and third

Solution:

In the first figure, 1 out of 3 parts are shaded. So, the fraction represented by it is 1 / 3.

In the second figure, 1 out of 6 parts are shaded. So, the fraction represented by it is 1 / 6.

In the third figure, 3 out of 9 parts are shaded. So it represents 3 / 9.

3 / 9 is equivalent to 1 / 3
[By dividing numerator and denominator by 3.]

So, first and third figures are equivalent.

7.
Which two figures represent equivalent fractions?  a. A, D b. B, D c. A, C d. B, C

Solution:

Figure A represents 3 / 4.

Figure B represents 2 / 4.

Figure C represents 3 / 4.

Figure D represents 1 / 4.

So, Figures A and C are equivalent fractions.

8.
Which of the figures represents equivalent fractions?  a. first and second b. second and third c. all the three figures d. first and third

Solution: Write the fractions for the given figure.

Amount shaded in the first and second figures is same.

So, 1 / 2 and 2 / 4 are equivalent fractions.

9.
Which set of numbers completes the pattern shown?
$\frac{1}{3}$ , $\frac{2}{6}$ , $\frac{3}{9}$ , $\frac{?}{12}$ , $\frac{?}{15}$ , $\frac{?}{18}$ a. 5, 6, and 8 b. 3, 4, and 5 c. 5, 6, and 7 d. 4, 5, and 6

Solution:

Let us use skip counting to find the set of numbers.

We observe from the pattern shown that the top numbers are counted by 1′s and the bottom numbers are skip counted by 3′s.

1 / 3 , 2 / 6 , 3 / 9 , 4 / 12 , 5 / 15 , 6 / 18
[The bottom numbers are skip counted by 3′s in order, so, count the top numbers in order, we get 4, 5, and 6.]

4, 5, and 6 is the set of numbers that completes the pattern shown.

10.
Choose the set of numbers that completes the pattern shown.
$\frac{2}{5}$ , $\frac{4}{10}$ , $\frac{6}{15}$ , $\frac{8}{?}$ , $\frac{10}{?}$ , $\frac{12}{?}$ a. 20, 25, and 35 b. 25, 30, and 35 c. 20, 25, and 30 d. 20, 30, and 40

Solution:

Let us use skip counting to find the set of numbers.

We observe from the pattern shown that the top numbers are skip counted by 2's and the bottom numbers are skip counted by 5's.

2 / 5 , 4 / 10 , 6 / 15 , 8 / 20 , 10 / 25 , 12 / 30
[The top numbers are skip counted by 2′s in order, so, count the bottom numbers in order, we get 20, 25, and 30.]

20, 25, and 30 is the set of numbers that completes the pattern shown.